Question

In how many ways can a cricket eleven be chosen out of a batch of 15 players?

• A. 1000
• B. 1665
• C. 225
• D. 1365
• E.

Hint:

Use the combination formula \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \) to find the number of ways to choose items.

Answer 1

The Correct Option is D

Step 1: The number of ways to select 11 players from a group of 15 is determined using the combination formula: \[ \binom{15}{11} = \binom{15}{4}. \] Since selecting 11 players from 15 is equivalent to selecting 4 players to be excluded, we use \( \binom{15}{4} \). Step 2: Compute \( \binom{15}{4} \): \[ \binom{15}{4} = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1}. \] \[ = \frac{32760}{24} = 1365. \] Thus, the total number of ways to form the team is 1365.